The ability to look in a mirror and realize that's a reflection of you, and not another being, is a big sign of being self aware. There is a clear line in the animal kingdom between animals that understand mirrors and those that don't.

Self-awareness is the state in which humans live their lives, in which they are able to think and be aware of the them that is doing the thinking. It is to be aware of oneself as an individual personality or entity. This goes beyond simple instinct found in other animals, and implies a deeper level of abstractthought (because one is thinking about the mind/what some might call soul, which is intangible).

It's something of a stretch to say that self-awareness is the state that allhumans live within. Many people live their entire lives too distracted by the pretty shiny things to bother questioning their own existence. On top of this, people aren't born self-aware. It's a long process, of living and living, and then one day 'waking up' to the world around you. It's easy to just go on unthinkingly, seeing as you've been doing it since pre-memory.